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Proof step 27 from proof challenge3 (previous step)

bst(t0), bst(t1), (r => mknode(r1, a, r2) * tr(r1, t0) * tr(r2, t1) * P)(H), (true * tr(r0, branch(t0 .butleftmost, a, t1)) * P)(H0), ∀ a0. a0 ∈ t0 → a0 < a, ∀ a0. a0 ∈ t1 → a < a0, ∀ a, c. a ∈ t0 ∧ c ∈ t1 → a < c, ∀ a0. ¬ a0 ∈ t0 ∨ ¬ a0 ∈ t1 ⊦ r = null, t0 = leaf, ¬ t0 .leftmost ∈ t1 ∧ t0 .leftmost ≠ a

User applied rule all left

And obtained the following new goals

Proof step 26:
bst(t0), bst(t1), (r => mknode(r1, a, r2) * tr(r1, t0) * tr(r2, t1) * P)(H), (true * tr(r0, branch(t0 .butleftmost, a, t1)) * P)(H0), t0 .leftmost ∈ t0 → t0 .leftmost < a, ∀ a0. a0 ∈ t0 → a0 < a, ∀ a0. a0 ∈ t1 → a < a0, ∀ a, c. a ∈ t0 ∧ c ∈ t1 → a < c, ∀ a0. ¬ a0 ∈ t0 ∨ ¬ a0 ∈ t1 ⊦ r = null, t0 = leaf, ¬ t0 .leftmost ∈ t1 ∧ t0 .leftmost ≠ a

Rule argument

[EXRARG : pos: left 5, [extquanttermlist: (t0 .leftmost) abort:F , discard:F , computed:F ]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (t0 .leftmost)]]